Honey, I'm sorry.
K. First, remember this little girl's world has imploded and she's very sad, scared, and angry. (I always think understanding the issue makes it easier to cope and think straight.)
She needs specific time for HER with YOU. The plain and simple truth is that NO ONE can ever take your place...makes things hard at times but there's just no getting around it.
So, when it's time for feeding baby, have her come sit by you and "help", when it's time for changing the diaper have her hand you the wet wipes, when it's time for nap go in an sing her to sleep while your holding baby instead of sending her to the bed, get a picture book and fill it with pictures of Daddy and pictures of her with Daddy that she can look at anytime...ANY,...basically just have her be your shadow with it comes to taking care of baby...tell "we" need to take care of "our" baby...or "YOUR" baby brother...let her hold him on the couch beside you with our arm around her back BARELY touching her so she thinks she's doing it all by herself--making sure she understands Mommy must sit beside her when she holds baby--she'll only want to do that for a very few minutes. Whenever the wee one is asleep, grab her and hug her, cuddle her, lay by her, take her into the kitchen for a snack, tickle her in another room...STEAL moments with her.
I want to suggest that time OUT doesn't "work" for you because it's the OUT she's responding to...she already feels like she's in time out--a BIG time out, and she's unhappy...and scared.
You may, instead, want to respond to the big problem when she's acting out rather than the symptom and hold her when she's out of control sympathizing with her that this is sad and hard and unfair but that Mommy and Daddy LOOOOOOOVE her sOOOOOOOO very, very much then get the pictures of Daddy to look at and/or suggest coloring Daddy a picture.
The other thing is that we tend to talk tooooo much. So many of us warn and warn and warn...yell, yell, yell, but don't actually invest ourselves into what we're saying, so our wee ones do not take us serious because, well, we're not taking ourselves serious. More action is required. If you tell her something and she chooses not to, instead of yelling/scolding simply get up and see that she does it while YOU model pleasant in control behavior. It'll be a challenge at first because you're feeling overwhelmed, but unfortunately THAT is a very big portion of the problem. I know, I understand...we're military, too, and we have a LOT of children...it's SO easy to be overwhelmed and allow things to go until I blow, but then, that's MY dis-function, not the children and I have to take responsibility for that cause I'm the leader, if I'm out of control how can I expect the followers not to be???
Hugs to you Mommy. This too shall pass. (yeah, I hated that saying when I was 22, too) :o)